• Journal of Korean Society of Coastal and Ocean Engineers
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• v.11 no.1
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• pp.7-19
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• 1999

The energy transfer between sea-wave components by way of nonlinear wave-wave interactions plays a central role in spectral evolution. Since huge calculation time is required to exact computation of the resulting Boltzmann integral, however, the exact nonlinear energy transfer has not been directly introduced into operational wave models. Thus, effective calculation methods were examined in the present study which exploit the scale property of a scattering coefficient and the detailed balance of interactions. The improved Webb's method (IWM) has inherent stability because singularities degenerate into a negligible point. The improved Masuda's method (IMM) makes a quasi-analytical treatment of the inherent singularities and requires only 1.3 seconds of computer time via Pentium 300MHz processor. The IMM is, therefore, projected to be very useful for theoretical researches in spectral evolution with fetch- or duration-limited situations.

• Journal of the Korean Vacuum Society
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• v.10 no.4
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• pp.424-430
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• 2001

An electron Boltzmann equation is solved numerically to calculate the electron energy distribution functions in plasma discharge which is generated by radio-frequency (RF) and microwave frequency electric field. The maintenance field strengths are determined self-consistently by solving the homogeneous electron Boltzmann equation in the Lorentz approximation expressed by 2nd order differential equation and an additional particle balance equation expressed by integro-differential equation. By using this numerical code, the electron energy distribution functions in argon discharge are calculated in the range from RF to microwave frequency. The influence of frequency of the HF electric field on the electron energy distribution functions and ionization rate are investigated.

• Proceedings of the Korean Nuclear Society Conference
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• 1996.05a
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• pp.173-178
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• 1996

특정한 방향성분에 대한 방향중성자속을 정의하는 방향차분 수송 방정식(discrete ordinates or S$_{N}$ transport equation)과 달리 방향변수를 구분된 방향영역에 대하여 적분하고, 해당 방향영역 내에서의 방향중성자속이 일정하다고 가정하는 영역상수법(piecewise constant method)을 이용하여 유사방향차분방정식(discrete ordinates-like equation)을 유도하여, 이를 Boltzmann 수송식과 2계 우성수송식(even-parity transport equation)에 적용하여 기존의 방향차분법의 단점인 광첨두현상(ray effects)을 감소시키고, 우성수송식의 교차미분항을 제거한 단순우성방정식(simplified even-parity equation)을 사용하여 광첨두현상을 제거하였다. 이는 단순우성방정식의 또 다른 장점을 제시한다.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.32 no.8
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• pp.12-19
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• 2004

Low-speed gas flows around a micro-scale flat plate are investigated using a kinetic theory analysis. The Boltzmann equation simplified by a collision model is solved by means of a finite difference approximation with the Discrete Ordinate method. Calculations are made for flows around a 5% flat plate with a finite length of 20 microns. The results are compared with those from the Information Preservation method and a continuum approach with slip boundary conditions. It is shown that three different approaches predict a similar basic flow patterns, while the results from the present method are more accurate than those from the other two methods in details.

• Journal of computational fluids engineering
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• v.1 no.1
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• pp.142-149
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• 1996

이차원 노즐을 통하여 저밀도 환경으로 팽창하는 희박류의 분석에 있어서 불연속좌표법과 결합된 유한차분법(finite-difference method coupled with the discrete-ordinate method, FDDO)과 직접모사법(direct-simulation Monte-Carlo method, DSMC)이 비교되었다. FDDO를 이용한 분석에서는 충돌적분모델을 도입하여 간단해진 볼츠만식(Boltzmann equation)이 불연속좌표법을 이용하여 물리적 공간에서는 연속이나 분자속도 공간에서는 불연속좌표로 표시되는 편미분방정식군으로 변환되어 유한차분법에의하여 수치해석 되었다. 직접모사법에서는 분자모델로 가변강구모델(variable hard sphere model, VHS)이, 충돌샘플링모델로는 비시계수법(no time counter method, NTC)이 채택되었다. 전혀 다른 두 가지 방법에 의한 노즐 내부에서의 유체흐름 해석결과는 매우 잘 일치하였으며, 노즐 외부의 plume 영역에서는 FDDO에 의한 해석결과가 직접모사법에 의한 해석결과에 비하여 약간 느린 팽창을 보였다.

• Journal of Energy Engineering
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• v.16 no.1 s.49
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• pp.46-52
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• 2007

The piecewise constant angular approximation is developed to replace the conventional angular quadrature sets in the solution of the second-order, multi-dimensional $S_{N}$ neutron transport equations. The newly generated quadrature sets by this method substantially mitigate ray effects and can be used in the same manner as the conventional quadrature sets are used. The discrete-ordinates and the piecewise-constant approximations are applied to both the first-order Boltzmann and the second-order form of neutron transport equations in treating angular variables. The result is that the mitigation of ray effects is only achieved by the piecewise-constant method, in which new angular quadratures are generated by integrating angle variables over the specified region. In other sense, the newly generated angular quadratures turn out to decrease the contribution of mixed-derivative terms in the even-parity equation that is one of the second-order neutron transport equation. This result can be interpreted as the entire elimination or substantial mitigation of ray effect are possible in the simplified even-parity equation which has no mixed-derivative terms.